A161875 Number of reduced words of length n in the Weyl group B_15.

1, 15, 119, 665, 2939, 10933, 35580, 103972, 277950, 689282, 1602727, 3523945, 7376794, 14784390, 28500705, 53054703, 95687255, 167682425, 286219155, 476896733, 777117381, 1240541355, 1942863430, 2989193690, 4523359115, 6739474341, 9896158795, 14333801669, 20495294280

Offset: 0

Author

John Cannon and N. J. A. Sloane, Nov 30 2009

Keywords

• nonn
• fini
• full

Comments

Computed with MAGMA using commands similar to those used to compute A161409.

References

• J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
• N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)

Links

• Robert Israel, Table of n, a(n) for n = 0..225

Crossrefs

Row n=15 of A128084.

Programs

Maple

G:= normal(mul((1-x^(2*k))/(1-x), k=1..15)):
seq(coeff(G, x, j), j=0..15^2); # Robert Israel, Nov 26 2017

Formula

G.f. for B_m is the polynomial Product_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.

Extensions

a(28) corrected by Sean A. Irvine, Mar 23 2025